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In [1]}, Berger associated to every \(p\) -adic de Rham representation \(V\)  a \((\varphi ,\nabla )\) -module \(\mathrm {N}_{\operatorname{dR}}(V)\)  over \(\mathcal {R}\) . Using the \(p\) LMT, he proved the \(p\) -adic monodromy theorem (previously a conjecture of Fontaine): every \(p\) -adic de Rham representation is potentially semistable.
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In [2]}, Marmora used the \(p\) LMT to construct a functor from the category of \((\varphi ,\nabla )\) -modules over \(\mathcal {R}\)  to that of \(K^{\operatorname{nr}}\) -valued Weil-Deligne representations of the Weil group \(\mathcal {W}_{\kappa (\!(t )\!)}\) , where \(K^{\operatorname{nr}}\)  is the maximal unramified extension of \(K\)  in a fixed algebraic closure of \(K\) .

